We have observed the breakup of the isobaric analog state at 11.193 MeV in 17F into three particles via three channels: proton decay to the α-unbound 9.585 MeV state in 16O; and α decay to the proton-unbound 2.365 and 3.502/3.547 MeV states in 13N. Laboratory α-particle spectra corresponding to these three modes have been generated in Monte Carlo simulations using single-channel, single- and multilevel R-matrix formulas. A fit of these spectra to the α spectrum resulting from a triple-coincidence measurement results in excellent agreement with the experimental spectrum and allows branching ratios to be deduced for these rare decay modes